Spectrum prediction in X-ray fluorescence analysis using Bayesian estimation
Spectrum prediction in X-ray fluorescence analysis using Bayesian estimation
复制标题
使用贝叶斯估计进行 X 射线荧光分析中的光谱预测
DOI：
10.1016/j.sab.2022.106593
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Tsuji Kouichi
中科院分区：
文献类型：
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作者：
Matsuyama Tsugufumi;Nakae Masanori;Murakami Masashi;Yoshida Yukihiko;Machida Masahiko;Tsuji Kouichi
减少测量时间在X射线荧光（XRF）分析中是重要的。Micro-XRF和共焦显微XRF分析已用于获得元素分布。因为这些技术是在扫描模式下执行的，所以减少每单位测量点的测量时间缩短了确定元素分布所需的时间。因此，我们将贝叶斯定理应用于XRF分析，以快速准确地估计XRF强度。在贝叶斯公式中，后验分布由似然函数和先验分布确定。由于所得到的后验函数是一个概率分布，因此将期望值作为最优值。我们认为，确定最佳的似然函数和先验分布，将有可能在一个长的测量时间快速估计的XRF光谱。在这项研究中，泊松分布和两个指数函数之和分别作为似然函数和先验分布。为了使用贝叶斯公式估计XRF光谱，使用实验室自制的微型XRF仪器分析了含有多种金属元素的标准玻璃样品和金属板。在1、3、5、7、10、20、30、60、100、180和3600秒的测量时间下进行微XRF测量，然后比较在使用和不使用贝叶斯估计的情况下获得的玻璃和金属样品中的元素的净强度。分别采用贝叶斯估计和不采用贝叶斯估计，在测量时间为1 s和7 s的情况下，康铜样品的Cu Kα净强度接近于3600 s的测量结果。因此，准确的XRF净强度测量的测量时间减少了> 85%。
Reducing the measurement time is important in X-ray fluorescence (XRF) analysis. Micro-XRF and confocal-micro XRF analyses have been used to obtain elemental distributions. Because these techniques are performed in the scanning mode, reducing the measurement time per unit measurement point shortens the time needed for determining elemental distributions. Therefore, we applied the Bayesian theorem to XRF analysis to quickly and accurately estimate the XRF intensity. In the Bayesian formula, the posterior distribution was determined by the likelihood function and prior distribution. Because the obtained posterior function was a probability distribution, the expected value was used as the optimal value. We considered that determining the optimal likelihood function and prior distribution would make it possible to quickly estimate the XRF spectrum in a long measurement time. In this study, the Poisson distribution and the sum of two exponential functions were employed as the likelihood function and prior distribution, respectively. To estimate the XRF spectrum using the Bayesian formula, a standard glass sample containing several metal elements and metal plate were analyzed using a laboratory-made micro-XRF instrument. The micro-XRF measurements were performed at measurement times of 1, 3, 5, 7, 10, 20, 30, 60, 100, 180, and 3600 s, and then the net intensities of the elements in the glass and metal samples obtained with and without the Bayesian estimation were compared. A Cu Kα net intensity for a constantan sample that was close to that obtained in 3600 s could be obtained with the measurement times of 1 and 7 s with and without the Bayesian estimation, respectively. Thus, the measurement time for an accurate XRF net intensity measurement was reduced by >85%.